Subdifferential formulas for a class of non-convex infimal convolutions

Abstract

In this paper, we provide a number of subdifferential formulas for a class of non-convex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time function. In particular, we generalize the results obtained recently by Zhang et al.

Keywords:

• infimal convolution
• minimal time function
• perturbed distance function
• perturbed minimal time function
• subdifferential

AMS Subject Classifications:

• 49J52
• 49J53
• 90C31

Notes

The research of Nguyen Mau Nam was partially supported by the USA National Science Foundation [grant number DMS-1411817]; the Simons Foundation [grant number #208785].